Factor. 10t^3 - 15t^2 + 6t - 9 ______

Identify Common Factors: Look for common factors in the first two terms and the last two terms separately. For the first two terms, 10t^3 and -15t^2, the common factor is 5t^2. For the last two terms, 6t and -9, the common factor is 3.Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms. 10t^3 - 15t^2 = 5t^2(2t - 3) 6t - 9 = 3(2t - 3)Rewrite Using Factored Terms: Now, we have the expression in the form of two binomials that share a common factor of (2t - 3). Rewrite the expression using the factored terms. 10t^3 - 15t^2 + 6t - 9 = 5t^2(2t - 3) + 3(2t - 3)Factor Out Common Binomial Factor: Factor out the common binomial factor (2t - 3) from both terms. 5t^2(2t - 3) + 3(2t - 3) = (5t^2 + 3)(2t - 3)

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10t^3 - 15t^2 + 6t - 9

Identify Common Factors: Look for common factors in the first two terms and the last two terms separately. $\newline$ For the first two terms, $10t^3$ and $-15t^2$ , the common factor is $5t^2$ . $\newline$ For the last two terms, $6t$ and $-9$ , the common factor is $3$ .
Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms. $\newline$ $10t^3 - 15t^2 = 5t^2(2t - 3)$ $\newline$ $6t - 9 = 3(2t - 3)$
Rewrite Using Factored Terms: Now, we have the expression in the form of two binomials that share a common factor of $(2t - 3)$ . Rewrite the expression using the factored terms. $10t^3 - 15t^2 + 6t - 9 = 5t^2(2t - 3) + 3(2t - 3)$
Factor Out Common Binomial Factor: Factor out the common binomial factor $(2t - 3)$ from both terms. $\newline$ $5t^2(2t - 3) + 3(2t - 3) = (5t^2 + 3)(2t - 3)$